Find the difference between the largest and smallest three-digit numbers for which

| August 7, 2021 | education

Find the difference between the largest and smallest three-digit numbers for which, when divided by 37, the quotient and remainder are the same.

Let the sought natural numbers a and b take such values ​​that when dividing a by 37, the quotient and remainder coincide and equal b, that is, a: 37 = b (rest b) or a = 38 ∙ b.

If b = 3, then a = 38 ∙ 3 = 114 – the smallest value of the three-digit number a, in which, when divided by 37, the quotient and remainder coincide.

If b = 26, then a = 38 ∙ 26 = 988 is the largest value of the three-digit number a, in which, when divided by 37, the quotient and remainder coincide.

988 – 114 = 874 – the difference between the largest and the smallest three-digit numbers in which, when divided by 37, the quotient and remainder coincide.

Answer: 874 is the difference between the largest and the smallest three-digit numbers, in which, when divided by 37, the quotient and remainder coincide.



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